CCCA Unit 5 – Transformations in the Coordinate PlaneDay 121 - Task

Name: ______Date: ______

Task: Exploring Reflections and Rotations

MCC9-12.G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle measure to those that do not (e.g., translation versus horizontal stretch).

MCC9-12.G.CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

MCC9-12.G.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

MCC9-12.G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

Reflections:

  1. On a piece of graph paper, graph the following points to create Square CDEF

C = (3, 0); D = (4, 1); E = (5, 0); F = (4, -1)

  1. Draw the line: x = 2.
  2. Using either Mira, patty paper or a transparency reflect the square over the x = 2 line.
  3. How have the new points changed?
  1. Using the original square, now reflect it over the y-axis.
  2. What has happened?

Why is this reflection further away than the last one?

What effect did changing the reflection line have?

  1. Write out the coordinates of each square.

Original Square / Reflection over x=2 / Reflection over y-axis
C / (___,___) / C’ / (___,___) / C’ / (___,___)
D / (___,___) / D’ / (___,___) / D’ / (___,___)
E / (___,___) / E’ / (___,___) / E’ / (___,___)
F / (___,___) / F’ / (___,___) / F’ / (___,___)

How far apart are the original square and the first reflection?

The original square and the second reflection?

How far is the original square from x=2 and how far is the first reflection from x=2?

How far is the original square from the y-axis and the second reflection and the y-axis?

  1. Draw the line y = 0.5x – 5. If you were to reflect the originalsquare over y = 0.5x – 5, predict where would the new vertices be?

Original Square / Prediction of Reflection over y = 0.5x – 5
C / (___,___) / C’ / (___,___)
D / (___,___) / D’ / (___,___)
E / (___,___) / E’ / (___,___)
F / (___,___) / F’ / (___,___)
  1. After you have made your prediction, using the Mira, patty paper, or transparency reflect the original square over the y = 0.5x – 5 line. How does your prediction compare with the actual reflection?
  1. Make a general conclusion about what happens to coordinates of a point when they are reflected over a line.

Rotations:

  1. Return to the original square.
  1. Plot the point B(2,0). Point B is now your point of rotation.
  1. Experiment with rotating the square about point B using either patty paper or a transparency. Try different numbers of degrees (less than 360) counter clockwise. Explain what is happening to the square and the points.
  1. Try rotating negative degrees (clockwise). What do you notice about 90 and –270? 180 and –180? 45 and –315?

Why do you think this is?

Are there any other pairs of measures that have the same phenomena? How could we predict additional pairs?

  1. Rotate the square, about point B, 270. Write down the new coordinates and compare them to the old coordinates.

Original Square / Rotation around B
C / (___,___) / C’ / (___,___)
D / (___,___) / D’ / (___,___)
E / (___,___) / E’ / (___,___)
F / (___,___) / F’ / (___,___)

What relationship is there between the points of the two figures?

  1. What conclusions can you make about what happens to coordinates when rotated?

EXTENSION

  1. Is there ever a time when a rotation is the same as a reflection? Explain.
  1. Create a sequence to support your answer to number 17.